Size effects in metal plasticity are widely accepted, and different theoretical approaches to handle the phenomenon are developing in the literature. The present work considers the Fleck and Willis (2009b) framework, and creates a new gradient enhanced rate-independent crystal plasticity FE-implementation. The study considers both energetic and dissipative gradient hardening and strengthening, and adopts a general form of the gradient enhanced effective slip rate. Monotonic and cyclic shearing of an infinite crystal slab containing a single slip system at an angle of 90° to the loading direction is a first benchmark case. A second case considers combined shear and tension in 2D of a constrained HCP single crystal. The HCP crystal is loaded in its basal plane by a so-called butterfly deformation path that inflicts repeated loading and unloading of the three crystallographic slip systems. Finally, the evolution and interaction of multiple plastic zones are demonstrated by considering a notched tensile sample. A direct comparison to visco-plastic (rate-dependent) simulations confirms that the proposed crystal plasticity framework forms a rate-independent limit for the gradient enhanced Fleck–Willis theory. The model response also reduces to that of conventional crystal plasticity in the limit of zero length parameters.

金属可塑性中的尺寸效应已被广泛接受，并且在文献中正在开发处理该现象的不同理论方法。目前的工作考虑了Fleck和Willis（2009b）框架，并创建了一种新的梯度增强型速率无关的晶体可塑性有限元实现方法。该研究考虑了能量梯度和耗散梯度的硬化和强化，并采用了梯度增强有效滑移率的一般形式。第一个基准情况是第一个基准情况，即无限大晶体平板的单调和循环剪切，该平板包含与载荷方向成90°角的单个滑移系统。第二种情况考虑受约束的HCP单晶在2D中的组合剪切和拉伸。HCP晶体通过所谓的蝴蝶形变形路径加载到其基础平面中，该路径导致三个晶体学滑移系统的重复加载和卸载。最后，通过考虑带缺口的拉伸样品，证明了多个塑料区域的演化和相互作用。与粘塑性（速率相关）模拟的直接比较证实，所提出的晶体可塑性框架形成了梯度增强的Fleck-Willis理论的速率独立极限。在零长度参数的限制下，模型响应也降低到传统的晶体可塑性。与粘塑性（速率相关）模拟的直接比较证实，所提出的晶体可塑性框架形成了梯度增强的Fleck-Willis理论的速率独立极限。在零长度参数的限制下，模型响应也降低到传统的晶体可塑性。与粘塑性（速率相关）模拟的直接比较证实，所提出的晶体可塑性框架形成了梯度增强的Fleck-Willis理论的速率独立极限。在零长度参数的限制下，模型响应也降低到传统的晶体可塑性。